Question

Use the law of exponents to rewrite and simplify the expression.

${\text{b}}^8{\left(2\text{b}\right)}^4$

Answer 1

To simplify the given expression:

Using the law of exponents to simplify the given expression in below:

$\begin{array}{rcl}{\text{b}}^8{\left(2\text{b}\right)}^4& =& {\text{b}}^8\left(2^4\times {\text{b}}^4\right)\left[\text{Power of a product rule:}{\left(\text{ab}\right)}^{\text{m}}={\left(\text{a}\right)}^{\text{m}}\times {\left(\text{b}\right)}^{\text{m}}\right]\\ & \Rightarrow & {\text{b}}^8{\left(2\text{b}\right)}^4={\text{b}}^8\left(16\times {\text{b}}^4\right)\left[\text{Simplifying}\right]\\ & \Rightarrow & {\text{b}}^8{\left(2\text{b}\right)}^4=16{\text{b}}^{8+4}\left[\text{Product rule}:{\text{a}}^{\text{m}}\times {\text{a}}^{\text{n}}={\text{a}}^{\text{m+n}}\right]\\ \therefore {\text{b}}^8{\left(2\text{b}\right)}^4& =& 16{\text{b}}^{12}\left[\text{Simplifying}\right]\end{array}$

Hence, the answer is $\mathbf{16}{\mathbf{\text{b}}}^{\mathbf{12}}$.